S.2 maths, please help

sinθ = opposite / hypotenuse, cosθ= adjacent / hypotenuse, tanθ= opposite / adjacent
adjacent^2 + 2^2 = 3^2 adjacent = √5　cosθ=√5/3 tanθ= 2/√5
留意 given sinθ (opposite 在分子) 應該知道tanθ的分子也是2

sin θ = 2/3
cosθ=√(1-sinθ)=√5/3
tanθ+1=1/cosθ
tanθ=9/5-1=4/5
tanθ=2/√5
(1-cosθ) tanθ
=[1-(√5/3)]^2*2/√5
=[1-2(√5/3)+5/9]*2/√5
=(28√5/45)-4/3

cosθ = √(1 - sin2θ) = √[1-(2/3)2] = √5/3
tanθ = sinθ / cosθ = (√5/3) / (2/3) = √5/2
(1 - cosθ )2 tanθ = (1 - √5/3)2 (√5/2)
= (1 + 5/9 - 2√5/3) √5/2
= 7√5/9 - 5/3

2008-06-09 17:36:17 補充：
Revised

tanθ = sinθ / cosθ = (2/3) / (√5/3) = 2/√5

(1 - cosθ )2 tanθ = (1 - √5/3)2 (2/√5)

= (1 + 5/9 - 2√5/3) 2/√5

= 28/(9√5) - 4/3

=28√5/45 - 4/3 ( correct answer)